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- Title
A space-time hp-interpolation-based certified reduced basis method for Burgers' equation.
- Authors
Yano, Masayuki; Patera, Anthony T.; Urban, Karsten
- Abstract
We present a space-time interpolation-based certified reduced basis method for Burgers' equation over the spatial interval (0, 1) and the temporal interval (0, T] parametrized with respect to the Peclet number. We first introduce a Petrov-Galerkin space-time finite element discretization which enjoys a favorable inf-sup constant that decreases slowly with Peclet number and final time T. We then consider an hp interpolation-based space-time reduced basis approximation and associated Brezzi-Rappaz-Raviart a posteriori error bounds. We describe computational offline-online decomposition procedures for the three key ingredients of the error bounds: the dual norm of the residual, a lower bound for the inf-sup constant, and the space-time Sobolev embedding constant. Numerical results demonstrate that our space-time formulation provides improved stability constants compared to classical L2-error estimates; the error bounds remain sharp over a wide range of Peclet numbers and long integration times T, in marked contrast to the exponentially growing estimate of the classical formulation for high Peclet number cases.
- Subjects
INTERPOLATION spaces; BURGERS' equation; SPACETIME; SPATIOTEMPORAL processes; GALERKIN methods; PECLET number
- Publication
Mathematical Models & Methods in Applied Sciences, 2014, Vol 24, Issue 9, p1903
- ISSN
0218-2025
- Publication type
Article
- DOI
10.1142/S0218202514500110